## Algebraic & Geometric Topology

### Hopf algebras and invariants of the Johnson cokernel

#### Abstract

We show that if $H$ is a cocommutative Hopf algebra, then there is a natural action of $Aut(Fn)$ on $H⊗n$ which induces an $Out(Fn)$ action on a quotient $H⊗n¯$. In the case when $H = T(V )$ is the tensor algebra, we show that the invariant $TrC$ of the cokernel of the Johnson homomorphism studied in Algebr. Geom. Topol. 15 (2015) 801–821 projects to take values in $Hvcd(Out(Fn);H⊗n¯)$. We analyze the $n = 2$ case, getting large families of obstructions generalizing the abelianization obstructions of Geom. Dedicata 176 (2015) 345–374.

#### Article information

Source
Algebr. Geom. Topol., Volume 16, Number 4 (2016), 2325-2363.

Dates
Revised: 20 January 2016
Accepted: 24 January 2016
First available in Project Euclid: 28 November 2017

https://projecteuclid.org/euclid.agt/1511895916

Digital Object Identifier
doi:10.2140/agt.2016.16.2325

Mathematical Reviews number (MathSciNet)
MR3546467

Zentralblatt MATH identifier
06627577

#### Citation

Conant, Jim; Kassabov, Martin. Hopf algebras and invariants of the Johnson cokernel. Algebr. Geom. Topol. 16 (2016), no. 4, 2325--2363. doi:10.2140/agt.2016.16.2325. https://projecteuclid.org/euclid.agt/1511895916

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